





"""simple docstring"""


from math import sqrt

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (
						    number >= 0
						), "'number' must been an int and positive"

						UpperCamelCase				:		Dict				   =			True

						# 0 and 1 are none primes.
						if number <= 1:
												UpperCamelCase				:		Optional[int]				   =			False

						for divisor in range(2							,     int(round(sqrt(SCREAMING_SNAKE_CASE     )     )     ) + 1     ):
												# if 'number' divisible by 'divisor' then sets 'status'
												# of false and break up the loop.
												if number % divisor == 0:
																		UpperCamelCase				:		Any				   =			False
																		break

    # precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ), "'status' must been from type bool"

						return status

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (n > 2), "'N' must been an int and > 2"

						# beginList: contains all natural numbers from 2 up to N
						UpperCamelCase				:		str				   =			list(range(2							,     n + 1     )     )

						UpperCamelCase				:		Optional[Any]				   =			[]  # this list will be returns.

						# actual sieve of erathostenes
						for i in range(len(SCREAMING_SNAKE_CASE     )     ):
												for j in range(i + 1							,     len(SCREAMING_SNAKE_CASE     )     ):
																		if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
																								UpperCamelCase				:		Union[str, Any]				   =			0

    # filters actual prime numbers.
						UpperCamelCase				:		str				   =			[x for x in begin_list if x != 0]

						# precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ), "'ans' must been from type list"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (n > 2), "'N' must been an int and > 2"

						UpperCamelCase				:		Dict				   =			[]

						# iterates over all numbers between 2 up to N+1
						# if a number is prime then appends to list 'ans'
						for number in range(2							,     n + 1     ):
												if is_prime(SCREAMING_SNAKE_CASE     ):
																		ans.append(SCREAMING_SNAKE_CASE     )

    # precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ), "'ans' must been from type list"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and number >= 0, "'number' must been an int and >= 0"

						UpperCamelCase				:		Tuple				   =			[]  # this list will be returns of the function.

						# potential prime number factors.

						UpperCamelCase				:		Union[str, Any]				   =			2

						UpperCamelCase				:		Tuple				   =			number

						if number == 0 or number == 1:
												ans.append(SCREAMING_SNAKE_CASE     )

						# if 'number' not prime then builds the prime factorization of 'number'
						elif not is_prime(SCREAMING_SNAKE_CASE     ):
												while quotient != 1:
																		if is_prime(SCREAMING_SNAKE_CASE     ) and (quotient % factor == 0):
																								ans.append(SCREAMING_SNAKE_CASE     )
																								quotient /= factor
																		else:
																								factor += 1

						else:
												ans.append(SCREAMING_SNAKE_CASE     )

						# precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ), "'ans' must been from type list"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (
						    number >= 0
						), "'number' bust been an int and >= 0"

						UpperCamelCase				:		List[Any]				   =			0

						# prime factorization of 'number'
						UpperCamelCase				:		int				   =			prime_factorization(SCREAMING_SNAKE_CASE     )

						UpperCamelCase				:		Optional[Any]				   =			max(SCREAMING_SNAKE_CASE     )

						# precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ), "'ans' must been from type int"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (
						    number >= 0
						), "'number' bust been an int and >= 0"

						UpperCamelCase				:		List[Any]				   =			0

						# prime factorization of 'number'
						UpperCamelCase				:		Tuple				   =			prime_factorization(SCREAMING_SNAKE_CASE     )

						UpperCamelCase				:		str				   =			min(SCREAMING_SNAKE_CASE     )

						# precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ), "'ans' must been from type int"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ), "'number' must been an int"
						assert isinstance(number % 2 == 0							,     SCREAMING_SNAKE_CASE     ), "compare bust been from type bool"

						return number % 2 == 0

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ), "'number' must been an int"
						assert isinstance(number % 2 != 0							,     SCREAMING_SNAKE_CASE     ), "compare bust been from type bool"

						return number % 2 != 0

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert (
						    isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (number > 2) and is_even(SCREAMING_SNAKE_CASE     )
						), "'number' must been an int, even and > 2"

						UpperCamelCase				:		Tuple				   =			[]  # this list will returned

						# creates a list of prime numbers between 2 up to 'number'
						UpperCamelCase				:		Dict				   =			get_prime_numbers(SCREAMING_SNAKE_CASE     )
						UpperCamelCase				:		Dict				   =			len(SCREAMING_SNAKE_CASE     )

						# run variable for while-loops.
						UpperCamelCase				:		Optional[int]				   =			0
						UpperCamelCase				:		Union[str, Any]				   =			None

						# exit variable. for break up the loops
						UpperCamelCase				:		str				   =			True

						while i < len_pn and loop:
												UpperCamelCase				:		Tuple				   =			i + 1

												while j < len_pn and loop:
																		if prime_numbers[i] + prime_numbers[j] == number:
																								UpperCamelCase				:		Any				   =			False
																								ans.append(prime_numbers[i]     )
																								ans.append(prime_numbers[j]     )

																		j += 1

												i += 1

						# precondition
						assert (
						    isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and (len(SCREAMING_SNAKE_CASE     ) == 2)
						    and (ans[0] + ans[1] == number)
						    and is_prime(ans[0]     )
						    and is_prime(ans[1]     )
						), "'ans' must contains two primes. And sum of elements must been eq 'number'"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ):
						assert (
						    isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and (numbera >= 0)
						    and (numbera >= 0)
						), "'number1' and 'number2' must been positive integer."

						UpperCamelCase				:		Optional[int]				   =			0

						while numbera != 0:
												UpperCamelCase				:		Union[str, Any]				   =			numbera % numbera
												UpperCamelCase				:		Any				   =			numbera
												UpperCamelCase				:		Optional[Any]				   =			rest

						# precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (
						    numbera >= 0
						), "'number' must been from type int and positive"

						return numbera

def      UpperCamelCase							(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ):
						assert (
						    isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and (numbera >= 1)
						    and (numbera >= 1)
						), "'number1' and 'number2' must been positive integer."

						UpperCamelCase				:		List[Any]				   =			1  # actual answer that will be return.

						# for kgV (x,1)
						if numbera > 1 and numbera > 1:
												# builds the prime factorization of 'number1' and 'number2'
												UpperCamelCase				:		Dict				   =			prime_factorization(SCREAMING_SNAKE_CASE     )
												UpperCamelCase				:		Optional[int]				   =			prime_factorization(SCREAMING_SNAKE_CASE     )

						elif numbera == 1 or numbera == 1:
												UpperCamelCase				:		Optional[Any]				   =			[]
												UpperCamelCase				:		List[str]				   =			[]
												UpperCamelCase				:		str				   =			max(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )

						UpperCamelCase				:		Optional[int]				   =			0
						UpperCamelCase				:		int				   =			0

						UpperCamelCase				:		int				   =			[]  # captured numbers int both 'primeFac1' and 'primeFac2'

						# iterates through primeFac1
						for n in prime_fac_a:
												if n not in done:
																		if n in prime_fac_a:
																								UpperCamelCase				:		Optional[Any]				   =			prime_fac_a.count(SCREAMING_SNAKE_CASE     )
																								UpperCamelCase				:		str				   =			prime_fac_a.count(SCREAMING_SNAKE_CASE     )

																								for _ in range(max(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )     ):
																														ans *= n

																		else:
																								UpperCamelCase				:		Tuple				   =			prime_fac_a.count(SCREAMING_SNAKE_CASE     )

																								for _ in range(SCREAMING_SNAKE_CASE     ):
																														ans *= n

																		done.append(SCREAMING_SNAKE_CASE     )

    # iterates through primeFac2
						for n in prime_fac_a:
												if n not in done:
																		UpperCamelCase				:		Optional[Any]				   =			prime_fac_a.count(SCREAMING_SNAKE_CASE     )

																		for _ in range(SCREAMING_SNAKE_CASE     ):
																								ans *= n

																		done.append(SCREAMING_SNAKE_CASE     )

    # precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (
						    ans >= 0
						), "'ans' must been from type int and positive"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (n >= 0), "'number' must been a positive int"

						UpperCamelCase				:		int				   =			0
						UpperCamelCase				:		Optional[Any]				   =			2  # this variable holds the answer

						while index < n:
												index += 1

												ans += 1  # counts to the next number

												# if ans not prime then
												# runs to the next prime number.
												while not is_prime(SCREAMING_SNAKE_CASE     ):
																		ans += 1

    # precondition
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and is_prime(
						    SCREAMING_SNAKE_CASE     ), "'ans' must been a prime number and from type int"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ):
						assert (
						    is_prime(SCREAMING_SNAKE_CASE     ) and is_prime(SCREAMING_SNAKE_CASE     ) and (p_number_a < p_number_a)
						), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

						UpperCamelCase				:		int				   =			p_number_a + 1  # jump to the next number

						UpperCamelCase				:		Optional[Any]				   =			[]  # this list will be returns.

						# if number is not prime then
						# fetch the next prime number.
						while not is_prime(SCREAMING_SNAKE_CASE     ):
												number += 1

						while number < p_number_a:
												ans.append(SCREAMING_SNAKE_CASE     )

												number += 1

												# fetch the next prime number.
												while not is_prime(SCREAMING_SNAKE_CASE     ):
																		number += 1

    # precondition
						assert (
						    isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and ans[0] != p_number_a
						    and ans[len(SCREAMING_SNAKE_CASE     ) - 1] != p_number_a
						), "'ans' must been a list without the arguments"

						# 'ans' contains not 'pNumber1' and 'pNumber2' !
						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (n >= 1), "'n' must been int and >= 1"

						UpperCamelCase				:		Tuple				   =			[]  # will be returned.

						for divisor in range(1							,     n + 1     ):
												if n % divisor == 0:
																		ans.append(SCREAMING_SNAKE_CASE     )

    # precondition
						assert ans[0] == 1 and ans[len(SCREAMING_SNAKE_CASE     ) - 1] == n, "Error in function getDivisiors(...)"

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (
						    number > 1
						), "'number' must been an int and >= 1"

						UpperCamelCase				:		Any				   =			get_divisors(SCREAMING_SNAKE_CASE     )

						# precondition
						assert (
						    isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and (divisors[0] == 1)
						    and (divisors[len(SCREAMING_SNAKE_CASE     ) - 1] == number)
						), "Error in help-function getDivisiors(...)"

						# summed all divisors up to 'number' (exclusive), hence [:-1]
						return sum(divisors[:-1]     ) == number

def      UpperCamelCase							(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ):
						assert (
						    isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and (denominator != 0)
						), "The arguments must been from type int and 'denominator' != 0"

						# build the greatest common divisor of numerator and denominator.
						UpperCamelCase				:		Dict				   =			gcd(abs(SCREAMING_SNAKE_CASE     )							,     abs(SCREAMING_SNAKE_CASE     )     )

						# precondition
						assert (
						    isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     )
						    and (numerator % gcd_of_fraction == 0)
						    and (denominator % gcd_of_fraction == 0)
						), "Error in function gcd(...,...)"

						return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (n >= 0), "'n' must been a int and >= 0"

						UpperCamelCase				:		Optional[int]				   =			1  # this will be return.

						for factor in range(1							,     n + 1     ):
												ans *= factor

						return ans

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						assert isinstance(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) and (n >= 0), "'n' must been an int and >= 0"

						UpperCamelCase				:		List[str]				   =			0
						UpperCamelCase				:		Union[str, Any]				   =			1
						UpperCamelCase				:		Dict				   =			1  # this will be return

						for _ in range(n - 1     ):
												UpperCamelCase				:		int				   =			ans
												ans += fiba
												UpperCamelCase				:		Dict				   =			tmp

						return ans






import unittest

from transformers import load_tool
from transformers.utils import is_torch_available


if is_torch_available():
		import torch

from transformers.testing_utils import require_torch

from .test_tools_common import ToolTesterMixin







@require_torch
class 					__lowercase  (						unittest.TestCase		,       _SCREAMING_SNAKE_CASE				):





							"""simple docstring"""

							def       snake_case			(					self						)		->       Optional[Any]:
														A      :					Optional[Any]      		=					load_tool('''text-to-speech'''						)
														self.tool.setup()




							def       snake_case			(					self						)		->       Union[str, Any]:
														# SpeechT5 isn't deterministic
														torch.manual_seed(0						)
														A      :					Optional[Any]      		=					self.tool('''hey'''						)
														A      :					List[str]      		=					result.to_raw()
														self.assertTrue(
														    torch.allclose(
														        resulting_tensor[:3]    ,						torch.tensor([-0.0_0_0_5_9_6_6_6_6_8_8_3_2_1_1_5_8_2_9, -0.0_0_0_3_6_5_7_6_4_0_1_9_0_7_9_5_0_6_4, -0.0_0_0_1_3_4_3_9_5_0_2_7_9_9_8_8_3_4_8_5]						)    ,						)						)






							def       snake_case			(					self						)		->       Optional[Any]:
														# SpeechT5 isn't deterministic
														torch.manual_seed(0						)
														A      :					int      		=					self.tool('''hey'''						)
														A      :					Any      		=					result.to_raw()
														self.assertTrue(
														    torch.allclose(
														        resulting_tensor[:3]    ,						torch.tensor([-0.0_0_0_5_9_6_6_6_6_8_8_3_2_1_1_5_8_2_9, -0.0_0_0_3_6_5_7_6_4_0_1_9_0_7_9_5_0_6_4, -0.0_0_0_1_3_4_3_9_5_0_2_7_9_9_8_8_3_4_8_5]						)    ,						)						)






